There are three coins. One is a two-headed coin ( having head on both faces ), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?

Let E1 denote the event of getting a two headed coin. let E2 denote the event of getting a biased coin which shows 75% of head. let E3 denote the event of getting a biased coin which shows 40% of tails. let A be the event of getting a two headed coin. P(E1)=1/3 P(E2)=1/3 P(E3)=1/3 P(A|E1)=2/2=1 P(A|E2)=75/100=3/4 P(A|E3)=100-40=60 =60/100=3/5 P(E1|A)=1/3*1/1/3*1+1/3*3/4+1/3*3/5=20/47 THEREFORE,THE OPTION A IS CORRECT.